Limits on Stellar Flybys in the Solar Birth Cluster

TL;DR

This work investigates how stellar flybys in the Sun's birth cluster could have excited outer solar system orbits and constrains the cluster environment via the product $\chi = n\tau$. It uses $n$-body simulations with randomly generated flyby histories, applied to two populations—the cold classical Kuiper belt and nine distant sednoids—to map flyby histories to limits on $\chi$. The cold classical analysis yields $\chi \lesssim 6\times 10^4\ \mathrm{Myr\; pc^{-3}}$, while the distant sednoids provide a stronger bound of $\chi \lesssim 5\times 10^3\ \mathrm{Myr\; pc^{-3}}$ (best-fit $\sim 1.5\times 10^3\ \mathrm{Myr\; pc^{-3}}$), owing to their lower binding energies. The results tighten our understanding of the Sun's birth environment and have implications for planetary-system formation scenarios, with future LSST discoveries expected to refine these limits further.

Abstract

The orbits of small bodies in the outer solar system are particularly sensitive to gravitational perturbations, including stellar flybys. Stellar clusters, with low velocity dispersions and high number densities, can be the source of strong and frequent flybys. As a result, we can infer what properties of the solar birth environment would be incompatible with the structure of the outer solar system observed today. Here, we explore with $n-$body simulations the implications of the low inclinations ($i < 20^{\circ}$) of the distant sednoids (objects with perihelia $q > 40 \mathrm{\; AU}$ and semimajor axes $a > 400 \mathrm{\; AU}$) for the properties of the solar birth cluster. We find that the existence of these orbits, if they were in place in the Sun's birth cluster phase, would limit the product of the stellar number density and the Sun's residence time in the birth cluster to $\lesssim 5 \times 10^3 \mathrm{\; Myr \; pc^{-3}}$, as compared to the weaker limit $\lesssim 5 \times 10^4 \mathrm{\; Myr \; pc^{-3}}$ implied by the low inclinations of the cold classical Kuiper belt.

Figures (3)

• Figure 1: Fraction of flyby histories that are compatible with the observed inclination distribution of cold classicals as a function of number of flybys with impact parameter $< 10^4\mathrm{\; AU}$. The initial condition for the inclination distribution is a Rayleigh distribution with a mode of $1.7^{\circ}$. The resulting upper limit on $\chi$, if we adopt a KS test threshold of $p_1 = 0.05$ and require at least $p_2 = 0.05$ of all simulations to exceed this threshold in order to remain compatible, is $\lesssim 6 \times 10^4 \mathrm{\;Myr\; pc^{-3}}$. The fraction starts near 1 because the KS test is relative to an assumed distribution of inclinations that matches the initial distribution.
• Figure 2: Example of inclination, perihelion, and semimajor axis evolution for each of the nine TNOs (median values in bold, individual clones in the background) in an individual simulation. Clones are only plotted and taken into the median calculation if they instantaneously pass the mask described in the text.
• Figure 3: Fraction of flyby histories that are compatible with the observed inclination distribution of distant sednoids (initial inclinations are set to zero) as a function of number of flybys with impact parameter $< 10^4\mathrm{\; AU}$. The resulting upper limit on $\chi$, if we adopt a KS test threshold of $p_1 = 0.05$ and require at least $p_2 = 0.05$ of all simulations to exceed this threshold in order to remain compatible, is $\lesssim 5 \times 10^3 \mathrm{\;Myr\; pc^{-3}}$. The fraction starts near zero because the initial inclinations are set at zero.